The death of the American painter Cy Twombly, at the age of 83, has ended one of the most distinguished artistic careers of the past half-century. Like a latter-day Ingres, he was an expatriate who lived in Italy, fascinated by the country's cultural heritage. Twombly's response to this stimulus was, however, anything but academic, as he expressed himself with a radical language of highly coloured stains and energetic brushwork. His success resulted from the combination of this exciting style with a subtle, original intellect, great self-belief and a measure of charm and good fortune.

Edwin Parker Twombly Jr was born in Lexington, Virginia. His father was a sports instructor and former baseball player whom Twombly admiringly described as still doing back flips at the age of 40: he was known as "Cy" after the legendary pitcher "Cyclone" Young. Twombly inherited his father's nickname, but not his athleticism.

After completing his initial training in Boston, in 1950 Cy junior joined the Art Students League in New York, the epicentre of abstract expressionism. Soon afterwards this influence followed Twombly to Black Mountain College in North Carolina, where his teachers included Robert Motherwell, although he was also inspired by the rector Charles Olson's interest in archetypal, symbolic imagery.

In such paintings as Min-Oe (1951) Twombly devised bold, symmetrical compositions, which, he suggested, were characteristic of both primitive and classical art. He also produced this effect in some of his sculptures, for example Untitled (Funerary Box for a Lime Green Python) (1954), where a pair of solemn-looking palm leaves gives the work a consciously ritualistic tone.

Twombly in 1958, the year after he moved to Italy from the US. Photograph: David Lees/Time & Life Pictures/Getty Images

Twombly's yearning for antiquity led inevitably to the transatlantic trip that he made in 1952 with a scholarship from the Museum of Fine Arts at Richmond, Virginia. With Robert Rauschenberg, whom he had met at the Art Students League, he travelled to Rome, the city in which he was to settle five years later, and, more surprisingly, Morocco.

Although the journey to North Africa was Rauschenberg's idea, it profoundly affected Twombly: he brought back a sketchbook filled with motifs and studies of materials, and subsequently produced expressive abstract canvases whose titles were taken from the Moroccan towns Tiznit and Quarzazat.

Most remarkably, in reaction against the taboos about left and right that he encountered on his travels, Twombly began to draw "as if with his left hand". By literally denying himself dexterity, he reduced his control of the creative process in a way that was analogous to surrealist techniques – he took this even further during his military service as a cryptographer in 1953-54 by working at night, in the dark.

Perhaps unsurprisingly, the joint exhibition that he held with Rauschenberg at New York's Stable Gallery in 1953 had some stormy reviews, with the Herald Tribune declaring that it was one of the two worst shows of the season.

Twombly remained undaunted: in certain pictures, such as Academy (1955), the odd defiant expletive emerges from what are otherwise abstract patterns. With these moments of crudity, the works destroy the conventional distinction between writing and painting – a theme that became even more obvious after Twombly's move to Rome in 1957.

Twombly's early years in Italy had an air of "la dolce vita" about them. It was in this period that he met Tatiana Franchetti, an Italian aristocrat, whom he married in 1959 in New York before buying a palazzo on the Via di Monserrato in Rome. During the late 1950s he also spent time by the sea, on the island of Procida and at Sperlonga, north of Naples, where he produced memorable images on canvas and paper.

As Twombly told the critic David Sylvester, "the Mediterranean is always just white, white, white": in the 24 drawings called Poems to the Sea the colour blue barely appears, and yet the cursory lines and spots create a sea of the mind's eye – hours of contemplation transformed into a few cryptic marks. With their textured, creamy backgrounds, the paintings inspired by Procida are also extremely evocative: parched cliff-tops in the Bay of Naples; crumbling plaster; the heat – it's all there if you look for it, though without that act of the imagination the charm quickly fades.

While many of Twombly's works have classical and literary associations – titles such as the School of Athens and inscribed lines by Sappho, Mallarmé, Keats or Catullus – not all of his oeuvre is so ethereal. Search hard, and phalluses appear among the squiggles (though American critics sometimes confused them with carrots or rockets), and in 1961 the juicy Ferragosto paintings recreated the mid-August holiday with lurid colours and brown scatological smears, applied once again with the left hand: Roland Barthes aptly described them as gestures of "dirtying", "deranging the morality of the body".

During these years in Italy, Twombly's output sometimes reflected developments in the rest of the world: for example, as minimalist artists were creating a stir in America and Europe, in the late 1960s Twombly executed six monochrome canvases, the Treatise on the Veil, which are completely blank apart from measurements written in crayon over the grey paint.

The austerity continued into the early 1970s with a series, dedicated to Twombly's late friend Nini Pirandello, characterised by subtle rhythmic patterns and muted colours, quite distinct from the baroque lushness of his earlier work. From the middle of the decade, however, a new variety and richness appeared. Twombly returned to sculpture, which he had abandoned in the late 1950s, producing objects redolent of classical architecture or ancient rites, while in his paintings a little later he introduced luminous, watery tones.

This tendency culminated in a spectacular sequence at the Venice Biennale in 1988. Inspired by the city's lagoon and canals, Twombly splashed acrylic on to canvases shaped like baroque ceiling paintings, as if Monet was meeting Jackson Pollock and Tiepolo.

Most brilliant of all, however, were two series from the 1990s (now in Tate Modern and the Museum of Modern Art in New York), which evoked the four seasons, and the stages of human life, with sensuous colours and characteristically enigmatic writing.

In the retrospective exhibition held at Tate Modern in 2008, these luxurious images contrasted starkly with the simpler blood-red Bacchus canvases, painted at the time of the Iraq war, in the following room. The Dionysian impulse remained a potent force in Twombly's work even as he was approaching 80. In contrast, his recently installed ceiling at the Salle des Bronzes in the Louvre offers a more serene vision of the classical tradition, with its lapidary inscriptions alluding to ancient Greek sculptors set against an intense blue background.

Although Twombly continued to live in Italy – much of the time in his house in Gaeta near Naples – he somehow remained very American. He often returned to Lexington, where he was still known to some as "Cy junior", and was happy to point out that the area has "more columns … than in all ancient Rome and Greece".

Entertaining, erudite and at times a little neurotic, Twombly was almost as intriguing in interviews as in his art. He certainly gave good copy – as well as commanding huge prices in the international art market. Twombly profited from the global economy, but as an individual and an artist he was very much of a particular milieu, that of the American sophisticate in Europe (although he hated the label "expatriate").

He forged a distinctive, at times thrilling, brand from references to the high culture of the past, only rarely referring to contemporary events or issues. Yet, despite this apparent remoteness from the present, he achieved early success by offering a clever alternative to abstract expressionism and managed to keep going long enough to come back into fashion. It is questionable whether such an esoteric artist would have so enduring a career if he started today.

Tatiana died in 2010. Twombly is survived by their son, Cyrus, who is also a painter; two grandchildren; and his partner, Nicola Del Roscio.